Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations

Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations

This paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic tran...

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Main Authors: Wenhua Qiu, Jianguo Si
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/386812
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spelling doaj-bc964df9b7a0401ab110a55f5dc98aca2020-11-25T00:10:45ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/386812386812Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic PerturbationsWenhua Qiu0Jianguo Si1School of Mathematics, Shandong University, Jinan, Shandong 250100, ChinaSchool of Mathematics, Shandong University, Jinan, Shandong 250100, ChinaThis paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic transformation. Hence, for the equation we can obtain a small almost-periodic solution.http://dx.doi.org/10.1155/2013/386812
collection DOAJ
language English
format Article
sources DOAJ
author Wenhua Qiu
Jianguo Si
spellingShingle Wenhua Qiu
Jianguo Si
Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations
Abstract and Applied Analysis
author_facet Wenhua Qiu
Jianguo Si
author_sort Wenhua Qiu
title Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations
title_short Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations
title_full Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations
title_fullStr Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations
title_full_unstemmed Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations
title_sort reducibility for a class of almost-periodic differential equations with degenerate equilibrium point under small almost-periodic perturbations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description This paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic transformation. Hence, for the equation we can obtain a small almost-periodic solution.
url http://dx.doi.org/10.1155/2013/386812
work_keys_str_mv AT wenhuaqiu reducibilityforaclassofalmostperiodicdifferentialequationswithdegenerateequilibriumpointundersmallalmostperiodicperturbations
AT jianguosi reducibilityforaclassofalmostperiodicdifferentialequationswithdegenerateequilibriumpointundersmallalmostperiodicperturbations
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